My car is making some sort of cyclic noise when it runs.
Cycling noises are common in cars with low refrigerant levels. When the refrigerant is low, the A/C system has a pressure sensor that turns the compressor off to avoid damaging it. Once the pressure gets to a good point again, the compressor turns back on until the pressure sensor turns it back off. The low refrigerant usually means there is a leak. Leaks can be minor or major and the system will need to be refilled to detect it. I suggest seeking help from a qualified mechanic, such as one from YourMechanic to help you determine the cause of the sound and the repairs needed.